We present a steady state model of pickup ion energization upstream of a cometary bow wave in order to investigate the effects of quasi-linear energy diffusion in the turbulence there. The model assumes that the ions are immediately isotropized at pickup, and it includes the effects of adiabatic acceleration in the slowing solar wind and of continual pickup of ions as the comet is approached. By taking all physical quantities to fall off as power laws with distance from the comet, an analytical expression is obtained for the distribution function of pickup ions in the reference frame moving with the solar wind. To illustrate the application of this model, we compare the model results to the observations of pickup ions at comet Giacobini-Zinner. At present, this is the only cometary encounter for which sufficient quantitative information is available. The model does not compare well with these observations, but it is not clear whether the differences are due to artificial problems in the model or the data analysis or to the action of other energization processes at this comet. Preliminary results from the Halley encounters appear to agree more closely with this model.